Calculate the time it takes light to travel a significant distance such as between objects in the Solar System

6.1.2 The Solar System

Objective

Calculate the time it takes light to travel a significant distance such as between objects in the Solar System.

Key concepts

• Light travels at a constant speed in vacuum.
• The speed of light, \$c\$, is \$3.00 \times 10^{8}\ \text{m s}^{-1}\$.
• Distances in the Solar System are usually given in kilometres (km) or astronomical units (AU).
• To find the travel time, convert the distance to metres and use \$t = d/c\$.

Speed of light

The accepted value for the speed of light in vacuum is

\$c = 3.00 \times 10^{8}\ \text{m s}^{-1}\$

Formula for light‑travel time

Time \$t\$ required for light to travel a distance \$d\$ is

\$t = \frac{d}{c}\$

where

• \$t\$ = time (seconds, minutes or hours as required)
• \$d\$ = distance (metres)
• \$c\$ = speed of light (\$3.00 \times 10^{8}\ \text{m s}^{-1}\$)

Typical Solar‑System distances

*Pluto is no longer classified as a planet but is often included for historical context.

Example calculation: Sun to Earth

1. Identify the distance: \$d = 1.496 \times 10^{11}\ \text{m}\$.
2. Insert into the formula:

   \$t = \frac{1.496 \times 10^{11}\ \text{m}}{3.00 \times 10^{8}\ \text{m s}^{-1}}\$

3. Calculate:

   \$t = 4.987 \times 10^{2}\ \text{s} \approx 499\ \text{s}\$

4. Convert to minutes:

   \$\frac{499\ \text{s}}{60\ \text{s min}^{-1}} \approx 8.3\ \text{min}\$

5. Result: Light takes about 8.3 minutes to travel from the Sun to Earth.

Step‑by‑step method for any pair of objects

1. Find the average distance between the two objects (usually given in km).
2. Convert the distance to metres: multiply by \$10^{3}\$.
3. Use the formula \$t = d / c\$ with \$c = 3.00 \times 10^{8}\ \text{m s}^{-1}\$.
4. Calculate \$t\$ in seconds.
5. If required, convert seconds to minutes (divide by 60) or hours (divide by 3600).

Practice questions

1. How long does it take light to travel from the Sun to Mars? Give your answer in minutes to one decimal place.
2. Calculate the light‑travel time from Earth to Jupiter. Express your answer in minutes.
3. A signal is sent from Earth to a spacecraft orbiting Saturn. If the distance is \$1.433 \times 10^{12}\ \text{m}\$, how many seconds will the signal take to reach the spacecraft?
4. Compare the light‑travel times from the Sun to Mercury and from the Sun to Neptune. Which is longer and by how many minutes?
5. If a hypothetical planet were located \$2.5 \times 10^{13}\ \text{m}\$ from the Sun, what would be the light‑travel time in hours?